The mean transverse momentum, \(\langle p_\mathrm {T}\rangle \) , of the charged-particle \(p_{\mathrm {T}}\)  spectrum
and its correlation with the charged-particle multiplicity \(N_{\mathrm {ch}}\)  carry an essential information on the underlying particle production mechanism.
This has been studied by many experiments at hadron colliders in
pp(\(\overline{\mathrm {p}}\) ) covering centre-of-mass energies from \({\sqrt{s\,} = 31~\textrm {GeV}}\)  up to
13\(~\mathrm {TeV}\)   [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]} as well as in Xe==Xe  [11]} and Pb==Pb  [12]} collisions at \({\sqrt{s_\mathrm {NN}\,} = 5.44~\mathrm {TeV}}\)  and 5.02\(~\mathrm {TeV}\) , respectively.
All experiments observed an increase of \(\langle p_\mathrm {T}\rangle \)  with \(N_{\mathrm {ch}}\)  in the central rapidity region, explained in the PYTHIA approach as a consequence of non-trivial colour reconnections (see discussion in Ref. [13]}).
While in the CGC approach \(\langle p_\mathrm {T}\rangle \)  is a universal function of the ratio of the charged-particle multiplicity to the transverse area of the collision [14]}, in the EPOS LHC model it is determined by the collective expansion [15]}.
For all collision systems, the \(\langle p_\mathrm {T}\rangle  \stackrel{=}{=}N_{\mathrm {ch}} \)  correlation is a basic observable for tuning or calibrating the theoretical models [16]}, a simple observable which allows extracting fundamental properties of a deconfined quark–gluon medium [17]}.
